He came to ballet late, beginning his studies at the age of 16 with evening classes at the Leningrad Ballet School. However, he progressed so quickly that he was soon transferred to day classes; he graduated in 1926 into the GATOB (later the Kirov). He specialized in character roles, although he also began to choreograph early on in his career. His first notable achievement was his collaboration with Kaplan, Vainonen, and Tchesnakov in the first production of Shostakovich's The Golden Age in 1930. His choreography frequently ran foul of the Soviet authorities, who were upset by his determination to be daring and innovative. He was once banned from working for six years.

He continued to dance with the Kirov until 1970, although there were several large gaps while he worked elsewhere. He was with the Bolshoi Ballet in Moscow from 1933 to 1942 as dancer and choreographer; he also worked as choreographer with the Isadora Duncan studio in Moscow in 1948. His major ballets include Shurale (mus. Yarullin, Kirov, 1950), Solveig (mus. Grieg, Maly Theatre, 1952), and Spartacus (Kirov, 1956), which was the first production to Khatchaturian's score. He created several ballets for the Kirov in the 1960s, including The Bedbug (1962), for which he chose a young Natalia Makarova in the lead, New Love (1963), and Land of Miracles (1967). He was also a popular concert artist, thanks to his skill at acrobatic dance, and created more than 100 concert pieces. It was Jacobson who made Vestris, the solo Baryshnikov danced when he won the International Ballet Competition in Moscow in 1969. One of Jacobson's miniatures was Rodin, with music by Debussy and inspired by Rodin sculptures at the Hermitage. In 1990 it entered the repertoire of San Francisco Ballet. He formed his own company, Choreographic Miniatures, in St Petersburg in 1970, although it appeared abroad as the Jacobson Ballet. After his death it became the State Ballet of Leningrad.